scholarly journals Estimating Relaxation Time and Fractionality Order Parameters in Fractional Non-Fourier Heat Conduction Using Conjugate Gradient Inverse Approach in Single and Three-Layer Skin Tissues

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1877
Author(s):  
Piran Goudarzi ◽  
Awatef Abidi ◽  
Seyed Abdollah Mansouri Mehryan ◽  
Mohammad Ghalambaz ◽  
Mikhail A. Sheremet
Keyword(s):  
Heat Conduction ◽  
Conjugate Gradient ◽  
Inverse Method ◽  
Single Layer ◽  
Constant Heat Flux ◽  
Phase Lag ◽  
Unknown Parameters ◽  
Conduction Model ◽  
Inverse Approach ◽  
Fourier Heat Conduction

In this work, the relaxation parameter (τ) and fractionality order (α) in the fractional single phase lag (FSPL) non-Fourier heat conduction model are estimated by employing the conjugate gradient inverse method (CGIM). Two different physics of skin tissue are chosen as the studied cases; single and three-layer skin tissues. Single-layer skin is exposed to laser radiation having the constant heat flux of Qin. However, a heat pulse with constant temperature is imposed on the three-layer skin. The required inputs for the inverse problem in the fractional diffusion equation are chosen from the outcomes of the dual phase lag (DPL) theory. The governing equations are solved numerically by utilizing implicit approaches. The results of this study showed the efficiency of the CGIM to estimate the unknown parameters in the FSPL model. In fact, obtained numerical results of the CGIM are in excellent compatibility with the FSPL model.

scholarly journals Fast Transient Thermal Analysis of Non-Fourier Heat Conduction Using Tikhonov Well-Conditioned Asymptotic Waveform Evaluation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sohel Rana ◽  
Jeevan Kanesan ◽  
Ahmed Wasif Reza ◽  
Harikrishnan Ramiah
Keyword(s):  
Thermal Analysis ◽  
Heat Conduction ◽  
Computational Time ◽  
Phase Lag ◽  
Conduction Model ◽  
Transient Thermal Analysis ◽  
Heat Conduction Model ◽  
Fourier Heat Conduction ◽  
Fast Transient ◽  
Transient Thermal

Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE) and finite element method (FEM). The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML), another well-conditioned scheme, called mass effect (ME) T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME) showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE) and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.

scholarly journals Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

2016 ◽  
Vol 63 (1) ◽  
pp. 129-144
Author(s):  
Mohammad Javad Noroozi ◽  
Seyfolah Saedodin ◽  
Davood Domiri Ganji
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Laser Source ◽  
Temperature Dependent ◽  
Conduction Model ◽  
Non Linear Equation ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Fourier Heat Conduction

Abstract The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

scholarly journals A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 876 ◽  
Author(s):  
Stanisław Kukla ◽  
Urszula Siedlecka
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Single Phase ◽  
Heat Conduction Problem ◽  
Expansion Method ◽  
Maximum Temperature ◽  
Phase Lag ◽  
Conduction Model ◽  
Laplace Transform Technique ◽  
Finite Medium

In this paper, an investigation of the maximum temperature propagation in a finite medium is presented. The heat conduction in the medium was modelled by using a single-phase-lag equation with fractional Caputo derivatives. The formulation and solution of the problem concern the heat conduction in a slab, a hollow cylinder, and a hollow sphere, which are subjected to a heat source represented by the Robotnov function and a harmonically varying ambient temperature. The problem with time-dependent Robin and homogenous Neumann boundary conditions has been solved by using an eigenfunction expansion method and the Laplace transform technique. The solution of the heat conduction problem was used for determination of the maximum temperature trajectories. The trajectories and propagation speeds of the temperature maxima in the medium depend on the order of fractional derivatives occurring in the heat conduction model. These dependencies for the heat conduction in the hollow cylinder have been numerically investigated.

Assessment of Models for Extracting Thermal Conductivity From Frequency Domain Thermoreflectance Experiments

2020 ◽  
Author(s):  
Siddharth Saurav ◽  
Sandip Mazumder
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Computational Domain ◽  
Fourier Heat Conduction

Abstract The Fourier heat conduction and the hyperbolic heat conduction equations were solved numerically to simulate a frequency-domain thermoreflectance (FDTR) experimental setup. Numerical solutions enable use of realistic boundary conditions, such as convective cooling from the various surfaces of the substrate and transducer. The equations were solved in time domain and the phase lag between the temperature at the center of the transducer and the modulated pump laser signal were computed for a modulation frequency range of 200 kHz to 200 MHz. It was found that the numerical predictions fit the experimentally measured phase lag better than analytical frequency-domain solutions of the Fourier heat equation based on Hankel transforms. The effects of boundary conditions were investigated and it was found that if the substrate (computational domain) is sufficiently large, the far-field boundary conditions have no effect on the computed phase lag. The interface conductance between the transducer and the substrate was also treated as a parameter, and was found to have some effect on the predicted thermal conductivity, but only in certain regimes. The hyperbolic heat conduction equation yielded identical results as the Fourier heat conduction equation for the particular case studied. The thermal conductivity value (best fit) for the silicon substrate considered in this study was found to be 108 W/m/K, which is slightly different from previously reported values for the same experimental data.

scholarly journals Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Jiawei Fu ◽  
Keqiang Hu ◽  
Linfang Qian ◽  
Zengtao Chen
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Intensity Factor ◽  
Functionally Graded ◽  
Conduction Model ◽  
Heat Conduction Model ◽  
Flux Intensity ◽  
Cylindrical Crack ◽  
Heat Flux Intensity ◽  
Fourier Heat Conduction

The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.

Stoneley Wave Generation in Joined Materials With and Without Thermal Relaxation Due to Thermal Mismatch

2007 ◽  
Vol 74 (5) ◽  
pp. 1019-1025 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Thermal Relaxation ◽  
Interface Temperature ◽  
Stoneley Wave ◽  
Asymptotic Results ◽  
Time Step ◽  
Conduction Model ◽  
Special Cases ◽  
Fourier Heat Conduction

Two perfectly bonded, thermoelastic half-spaces differ only in their thermal parameters. Their governing equations include as special cases the Fourier heat conduction model and models with either one or two thermal relaxation times. An exact solution in transform space for the problem of line loads applied to the interface is obtained. Even though the elastic properties of the half-spaces are identical, a Stoneley function arises, and conditions for the existence of roots are more restrictive than for the isothermal case of two elastically dissimilar half-spaces. Moreover, roots may be either real or imaginary. An exact expression for the time transform of the Stoneley residue contribution to interface temperature change is derived. Asymptotic results for the inverse that, valid for either very short or very long times after load application, is obtained and show that, for long times, residue contributions for all three special cases obey Fourier heat conduction. Short-time results are sensitive to case differences. In particular, a time step load produces a propagating step in temperature for the Fourier and double-relaxation time models, but a propagating impulse for the single-relaxation time model.

Thermoelastic Actuation: Solution for Circular Composite Plates With Application in MEMS

2002 ◽  
Author(s):  
Venkataraman Chandrasekaran ◽  
Mark Sheplak ◽  
Louis N. Cattafesta ◽  
Bhavani V. Sankar
Keyword(s):  
Heat Conduction ◽  
Joule Heating ◽  
Plate Theory ◽  
Composite Plates ◽  
Mechanical Analysis ◽  
Conduction Model ◽  
Time Harmonic ◽  
Out Of Plane ◽  
Fourier Heat Conduction ◽  
Analytical Expressions

This paper presents the dynamic analysis of a thermoelastically actuated circular composite diaphragm, for MEMS applications. The diaphragm is used as an acoustic transmitter, actuated at ultrasonic frequencies via a diffused surface heater at its center. The principle of operation of the thermal actuator is the generation of an oscillating temperature gradient across the diaphragm cross-section due to Joule heating of the diffused heater, creating a thermal moment that results in out-of-plane bending of the diaphragm. The mechanical analysis of the diaphragm, modeled as a composite plate, is based on the classical laminated plate theory. The time harmonic heat conduction resulting from the Joule heating of the diffused surface heater, modeled as a surface heat flux input, is analyzed using the Fourier heat conduction model. Analytical expressions have been obtained for the temperature distribution, and the resulting thermal moment, and plate deflection.

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